No, at least no legal way. Or well, you could create an other startup window (with a C/C++ program that can be used as a launcher for your game), that covers the engine startup window. I think jcl once said that it would be okay if this window would still contain the Lite-C Logo. But to be sure you better ask.
(Be aware that if you try to hide the startup window without showing the Lite-C Logo somewhere else, that would be illegal!)